Kepler's Third Law Calculator

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Satellite Orbital Characteristics

Geostationary Orbit

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✖Mean Motion is angular speed required for a body to complete an orbit, assuming constant speed in circular orbit that takes same time as variable speed elliptical orbit of actual body.ⓘ Mean Motion [n]

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✖The Semi major axis can be used to determine the size of satellite's orbit. It is half of the major axis.ⓘ Kepler's Third Law [a_semi]

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Formula

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Kepler's Third Law

Formula

`"a"_{"semi"} = ("[GM.Earth]"/"n"^2)^(1/3)`

Example

`"581706.9km"=("[GM.Earth]"/("0.045rad/s")^2)^(1/3)`

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Kepler's Third Law Solution

STEP 0: Pre-Calculation Summary

Formula Used

Semi Major Axis = ([GM.Earth]/Mean Motion^2)^(1/3)
a_semi = ([GM.Earth]/n^2)^(1/3)
This formula uses 1 Constants, 2 Variables

Constants Used

[GM.Earth] - Earth’s Geocentric Gravitational Constant Value Taken As 3.986004418E+14

Variables Used

Semi Major Axis - (Measured in Kilometer) - The Semi major axis can be used to determine the size of satellite's orbit. It is half of the major axis.
Mean Motion - (Measured in Radian per Second) - Mean Motion is angular speed required for a body to complete an orbit, assuming constant speed in circular orbit that takes same time as variable speed elliptical orbit of actual body.

STEP 1: Convert Input(s) to Base Unit

Mean Motion: 0.045 Radian per Second --> 0.045 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a_semi = ([GM.Earth]/n^2)^(1/3) --> ([GM.Earth]/0.045^2)^(1/3)

Evaluating ... ...

a_semi = 581706.945697113

STEP 3: Convert Result to Output's Unit

581706945.697113 Meter -->581706.945697113 Kilometer (Check conversion here)

FINAL ANSWER

581706.945697113 ≈ 581706.9 Kilometer <-- Semi Major Axis

(Calculation completed in 00.004 seconds)

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Bipin Tripathi Kumaon Institute of Technology (BTKIT), Dwarahat

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< 16 Satellite Orbital Characteristics Calculators

Position Vector

Go Position Vector = (Major Axis*(1-Eccentricity^2))/(1+Eccentricity*cos(True Anomaly))

Kepler's First Law

Go Eccentricity = sqrt((Semi Major Axis^2-Semi Minor Axis^2))/Semi Major Axis

Mean Anomaly

Go Mean Anomaly = Eccentric Anomaly-Eccentricity*sin(Eccentric Anomaly)

True Anomaly

Go True Anomaly = Mean Anomaly+(2*Eccentricity*sin(Mean Anomaly))

Universal Time

Go Universal Time = (1/24)*(Time in Hour+(Time in Minutes/60)+(Time in Seconds/3600))

Reference Time in Julian Centuries

Go Reference Time = (Julian Day-Julian Day Reference)/Julian Century

Julian Century

Go Julian Century = (Julian Day-Julian Day Reference)/Reference Time

Julian Day

Go Julian Day = (Reference Time*Julian Century)+Julian Day Reference

Nominal Mean Motion

Go Nominal Mean Motion = sqrt([GM.Earth]/Semi Major Axis^3)

Mean Motion of Satellite

Go Mean Motion = sqrt([GM.Earth]/Semi Major Axis^3)

Local Sidereal Time

Go Local Sidereal Time = Greenwich Sidereal Time+East Longitude

Kepler's Third Law

Go Semi Major Axis = ([GM.Earth]/Mean Motion^2)^(1/3)

Range Vector

Go Range Vector = Satellite Radius Vector-[Earth-R]

Orbital Period of Satellite in Minutes

Go Orbital Period in Minutes = 2*pi/Mean Motion

Anomalistic Period

Go Anomalistic Period = (2*pi)/Mean Motion

Universal Time Degree

Go Universal Time Degree = (Universal Time*360)

Kepler's Third Law Formula

Semi Major Axis = ([GM.Earth]/Mean Motion^2)^(1/3)
a_semi = ([GM.Earth]/n^2)^(1/3)

What are Kepler's laws?

Kepler's first law: The orbit of a planet is an ellipse with the sun at one of the foci. Kepler's second law: The line joining the planet and the sun sweeps equal areas in equal intervals of time.

How to Calculate Kepler's Third Law?

Kepler's Third Law calculator uses Semi Major Axis = ([GM.Earth]/Mean Motion^2)^(1/3) to calculate the Semi Major Axis, The Kepler's Third Law formula is defined as the squares of the orbital periods of the planets are directly proportional to the cubes of the semi-major axes of their orbits. Kepler's Third Law implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit. Semi Major Axis is denoted by a_semi symbol.

How to calculate Kepler's Third Law using this online calculator? To use this online calculator for Kepler's Third Law, enter Mean Motion (n) and hit the calculate button. Here is how the Kepler's Third Law calculation can be explained with given input values -> 0.581707 = ([GM.Earth]/0.045^2)^(1/3).

FAQ

What is Kepler's Third Law?

The Kepler's Third Law formula is defined as the squares of the orbital periods of the planets are directly proportional to the cubes of the semi-major axes of their orbits. Kepler's Third Law implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit and is represented as a_semi = ([GM.Earth]/n^2)^(1/3) or Semi Major Axis = ([GM.Earth]/Mean Motion^2)^(1/3). Mean Motion is angular speed required for a body to complete an orbit, assuming constant speed in circular orbit that takes same time as variable speed elliptical orbit of actual body.

How to calculate Kepler's Third Law?

The Kepler's Third Law formula is defined as the squares of the orbital periods of the planets are directly proportional to the cubes of the semi-major axes of their orbits. Kepler's Third Law implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit is calculated using Semi Major Axis = ([GM.Earth]/Mean Motion^2)^(1/3). To calculate Kepler's Third Law, you need Mean Motion (n). With our tool, you need to enter the respective value for Mean Motion and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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